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Bank of America, the biggest bank in the state and nation, is considering charging some checking customers additional fees starting next year as it tries to offset the cost of complying with new financial rules.

Bank officials said yesterday they are still testing various pricing models around the country. So far, they said, they have ruled out charging all checking account customers a blanket fee, and are opting instead to offer a menu of account options.

For example, some customers of its basic checking service could be asked to pay a monthly maintenance fee or other charge to cover the cost of servicing their account. But the bank could waive fees for customers who use self less-expensive, self-service options — online banking or ATMs, for instance —rather than tellers, who regularly use debit and credit cards, or who agree to do business with the bank in other ways.

“Each offering provides a distinct value, and there’s a cost that comes with that value,’’ said Bank of America spokeswoman Anne Pace. “Customers will have more choices in how they want to pay for that value.’’

The move was first reported by The Wall Street Journal yesterday.

Bank of America, like many banks, is looking for new revenues as it faces additional financial regulations, which, for example, limit overdraft fees on debit cards. In addition, the bank faces increased assessments from the Federal Deposit Insurance Corp. to replenish the nation’s deposit insurance fund.

Bank of America has elected to go beyond the new federal limits by scrapping most of its overdraft fees altogether, winning praise from consumer advocates. But eliminating those fees will cost $160 million a quarter, the bank estimates.

Altogether, the company estimated that it will collect about $600 million less a quarter in service fees once the new financial rules go into effect this year.

“You should expect that customers will have a choice of banking more efficiently, bringing more relationships to us, or paying a maintenance fee.’’

Like many banks, Bank of America already charges a monthly maintenance fee for many standard accounts. But most customers can easily avoid the fee by maintaining a minimum balance or meeting other requirements, essentially giving them free basic checking.

Other major banks are also expected to implement new fees or find other ways to increase their revenue in coming months.

TD Bank spokeswoman Rebecca S. Acevedo said: “We are weighing our options but haven’t made any decisions in this area yet.’’